University of California, Berkeley

Fall 2009

This is an introductory course on complex analysis.

The official prerequisite for taking this course is Math 104: Introduction to Analysis.

- 12/08/09: Office hours 1–2PM, Wed, Dec 09 and 1–3PM, Tue, Dec 15.
- 12/05/09: Revision lecture in 9 Evans, 1–2PM, Mon, Dec 07.
- 12/05/09: Problem Set 10 and solutions posted.
- 12/05/09: Final Exam to be held in 2 Leconte from 5–8PM, Wed, Dec 16.
- 11/30/09: Solutions to Problem Set 9 posted.
- 11/23/09: Solutions to Problem Set 8 posted.
- 11/20/09: Problem Set 9 posted.
- 11/17/09: Solutions to Problem Set 7 posted.
- 11/14/09: Solutions to Problem Set 6 posted.
- 11/14/09: Problem Set 8 posted.
- 11/08/09: Problem Set 7 posted.
- 11/01/09: Problem Set 6 posted.
- 10/24/09: Solutions to Problem Set 5 posted.
- 10/21/09: Office hours next week: 2–3PM on Mon, Oct 26 and Tue, Oct 27.
- 10/21/09: Solutions to Problem Set 4 posted.
- 10/19/09: Midterm Exam to be held in 106 Stanley from 1–2PM, Wed, Oct 28.
- 10/19/09: Solutions to Problem Set 3 posted.
- 10/17/09: Problem Set 5 posted.
- 10/12/09: Mon 12–1PM office hour moved to Fri 2–3PM.
- 10/03/09: Problem Set 4 posted.
- 09/29/09: Solutions to Problem Set 2 posted.
- 09/26/09: Problem Set 3 posted.
- 09/18/09: Office hours next week: MW 4–5PM, W 2–3PM.
- 09/17/09: Problem Set 2 posted.
- 09/11/09: Solutions to Problem Set 1 posted.
- 09/05/09: Problem Set 1 posted.
- 08/14/09: This class is currently oversubscribed. Prof. Richard Borcherds will teach the same course 3:30–5, TT in 123 Wheeler Hall. Please attend his lectures instead if you are still on the waiting list.
- 08/14/09: Check this page regularly for announcements.

**Location:** Evans Hall,
Room 9

**Times:** 1:00–2:00 PM on Mon/Wed/Fri

**Instructor:** Lek-Heng
Lim

Evans Hall, Room 873

`lekheng(at)math.berkeley.edu`

(510) 642-8576

**Office hours:** 12:00–1:00 PM, Mon and Wed, 2:00 AM–3:00
PM, Wed

- Analytic functions of a complex variable
- Cauchy's integral theorem
- Power series
- Laurent series
- Singularities of analytic functions
- Residue theorem with application to definite integrals
- Additional topics

Homework will be assigned once a week and will be due the following week (except possibly in the weeks when there is a midterm). Collaborations are permitted but you will need to write up your own solutions.

- Problem Set 10: PDF (posted: Dec 05; not collected); Solutions: PDF (posted: Dec 05)
- Problem Set 9: PDF (posted: Nov 20; due: Nov 30); Solutions: PDF (posted: Nov 30)
- Problem Set 8: PDF (posted: Nov 14; due: Nov 20); Solutions: PDF (posted: Nov 23)
- Problem Set 7: PDF (posted: Nov 08; due: Nov 13)); Solutions: PDF (posted: Nov 17)
- Problem Set 6: PDF (posted: Nov 01; due: Nov 06); Solutions: PDF (posted: Nov 14)
- Problem Set 5: PDF (posted: Oct 17; due: Oct 23); Solutions: PDF (posted: Oct 24)
- Problem Set 4: PDF (posted: Oct 03; due: Oct 07); Solutions: PDF (posted: Oct 21)
- Problem Set 3: PDF (posted: Sep 26; due: Oct 02); Solutions: PDF (posted: Oct 19)
- Problem Set 2: PDF (posted: Sep 17; due: Sep 25); Solutions: PDF (posted: Sep 29)
- Problem Set 1: PDF (posted: Sep 05; due: Sep 11); Solutions: PDF (posted: Sep 11)

**Bug report** on the problem sets or the solutions:
`lekheng(at)math.berkeley.edu`

- J.D. Gray and S.A. Morris,
"When
is a function that satisfies the
Cauchy-Riemann equations analytic?,"
*American Mathematical Monthly*,**85**(1978), no. 4, pp. 246–256.

- M.G. Arsove,
"On
the definition of an analytic function,"
*American Mathematical Monthly*,**62**(1955), no. 1, pp. 22–25.

- J. B. Deeds,
"The Cayley–Hamilton theorem via complex
integration,"
*American Mathematical Monthly*,**78**(1971), no. 9, pp. 1003–1004.

- Course homepage from Fall 2008.

**Grade composition:** 40% Homework, 20% Midterm, 40% Final

The second book is optional. It's more advanced than the first book but covers the same basic materials. You can choose either of them — buy the second book if you're looking for something that remains useful in a graduate course on complex analysis.